Edit Profile (opens in new tab) Golub, Gene Howard (b. 1932 d. 2007) Co-Author Distance Author ID: golub.gene-h Published as: Golub, Gene H.; Golub, G. H.; Golub, Gene; Golub, G. more...less External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 258 Publications since 1961, including 14 Books 9 Contributions as Editor Biographic References: 5 Publications Co-Authors: 186 Co-Authors with 244 Joint Publications 6,135 Co-Co-Authors all top 5 Co-Authors 18 single-authored 10 Van Loan, Charles Francis 9 Boley, Daniel L. 8 Bai, Zhongzhi 8 Concus, Paul 8 O’Leary, Dianne P. 7 Gander, Walter 7 Meurant, Gérard A. 7 Milanfar, Peyman 6 Calvetti, Daniela 6 Elhay, Sylvan 6 Elman, Howard C. 6 Reichel, Lothar 5 Chan, Tony Fan-Cheong 5 Chu, Moody T. 5 Greif, Chen 5 Kautsky, Jaroslav 5 Law, Kincho H. 5 Plemmons, Robert James 5 Van Dooren, Paul M. 5 von Matt, Urs 5 Zha, Hongyuan 4 Arbenz, Peter 4 Bartels, Richard Harold 4 Benzi, Michele 4 Ortega, James M. 4 Van Barel, Marc 4 Vandebril, Raf 4 Varah, James M. 4 Zhang, Tong 3 Bai, Zhaojun 3 Bertaccini, Daniele 3 Chandrasekaran, Shivkumar 3 Fischer, Bernd 3 Funderlic, Robert E. 3 Gu, Ming 3 Hansen, Per Christian 3 LeVeque, Randall J. 3 Luk, Franklin T. 3 Nash, Stephen G. 3 Ng, Michael Kwok-Po 3 Overton, Michael L. 3 Saunders, Michael A. 3 Sayed, Ali H. 3 Serra-Capizzano, Stefano 3 Strebel, Rolf 3 Van der Vorst, Henk Albertus 3 Wathen, Andrew John 3 Wilkinson, James Hardy 3 Ye, Qiang 3 Yuan, Jinyun 2 Berry, Michael W. 2 Björck, Åke 2 Buzbee, Billy L. 2 Chan, Raymond Hon-Fu 2 Chang, Xiaowen 2 Cuyt, Annie A. M. 2 Dahlquist, Germund 2 de Boor, Carl 2 De Moor, Bart L. R. 2 Elad, Michael 2 Fierro, Ricardo D. 2 Gautschi, Walter 2 Greenbaum, Anne 2 Gutknecht, Martin H. 2 Hald, Ole Hansen 2 Kågström, Bo 2 Lee, Chris P. 2 Li, Chi-Kwong 2 Liao, Li-Zhi 2 Mastronardi, Nicola 2 Mulet, Pep 2 Ram, Yitshak M. 2 Seneta, Eugene 2 Sølna, Knut 2 Stewart, Gilbert Wright 2 Tang, Wei-Pai 2 Underwood, Richard 2 Varga, Richard Steven 2 Verdonk, Brigitte M. 2 Widlund, Olof B. 2 Wu, Xiaonan 2 Zenios, Stefanos A. 2 Zhang, Zhenyue 1 Alter, Orly 1 Andersson, Lars-Erik 1 Baglama, James 1 Beckermann, Bernhard 1 Björk, Åke 1 Bochev, M. A. 1 Boutry, Gregory 1 Brent, Richard Peirce 1 Businger, P. A. 1 Carey, Cheryl M. M. 1 Cecilio, W. A. G. 1 Chu, Delin 1 Cline, Alan K. 1 Comon, Pierre 1 Cottle, Richard W. 1 Cuminato, José Alberto 1 Dorr, Fred W. ...and 88 more Co-Authors all top 5 Serials 28 SIAM Journal on Matrix Analysis and Applications 16 BIT 15 Numerische Mathematik 15 Linear Algebra and its Applications 14 SIAM Journal on Scientific Computing 13 Mathematics of Computation 11 Numerical Algorithms 8 SIAM Journal on Numerical Analysis 5 Journal of Computational and Applied Mathematics 5 SIAM Review 4 SIAM Journal on Scientific and Statistical Computing 3 Systems & Control Letters 3 Communications of the ACM 3 Numerical Linear Algebra with Applications 2 Bulletin of the Australian Mathematical Society 2 IMA Journal of Numerical Analysis 2 Inverse Problems 2 Calcolo 2 Journal of Econometrics 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 IEEE Transactions on Image Processing 2 Internet Mathematics 2 Acta Numerica 2 Johns Hopkins Series in the Mathematical Sciences 1 The American Statistician 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 ACM Transactions on Mathematical Software 1 Aplikace Matematiky 1 Applied Mathematics and Optimization 1 Computing 1 IEEE Transactions on Automatic Control 1 IEEE Transactions on Computers 1 International Journal for Numerical Methods in Engineering 1 Journal of the American Statistical Association 1 Technometrics 1 SIAM Journal on Algebraic and Discrete Methods 1 Applied Numerical Mathematics 1 IEEE Transactions on Signal Processing 1 IEEE Transactions on Circuits and Systems. II: Analog and Digital Signal Processing 1 Journal of Statistical Computation and Simulation 1 Mitteilungen der Mathematischen Gesellschaft in Hamburg 1 Proceedings of the National Academy of Sciences of the United States of America 1 ETNA. Electronic Transactions on Numerical Analysis 1 Annals of Numerical Mathematics 1 Journal of the Society for Industrial & Applied Mathematics 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Berliner Studienreihe zur Mathematik 1 Collection de la Direction des Études et Recherches d’Électricité de France 1 The IMA Volumes in Mathematics and its Applications 1 ISNM. International Series of Numerical Mathematics 1 MAA Studies in Mathematics 1 NATO ASI Series. Series E. Applied Sciences 1 NATO ASI Series. Series F. Computer and Systems Sciences 1 Proceedings of Symposia in Applied Mathematics 1 Publications of the Mathematics Research Center, The University of Wisconsin - Madison 1 Texts and Readings in Mathematics 1 Annals of Mathematical Statistics 1 Journal of the Society for Industrial and Applied Mathematics. Series B, Numerical Analysis 1 Numerical Mathematics and Scientific Computation 1 Princeton Series in Applied Mathematics all top 5 Fields 216 Numerical analysis (65-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 26 Partial differential equations (35-XX) 21 Statistics (62-XX) 18 Computer science (68-XX) 11 General and overarching topics; collections (00-XX) 11 History and biography (01-XX) 9 Operations research, mathematical programming (90-XX) 8 Approximations and expansions (41-XX) 6 Fluid mechanics (76-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 5 Probability theory and stochastic processes (60-XX) 5 Systems theory; control (93-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of deformable solids (74-XX) 1 Functions of a complex variable (30-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 237 Publications have been cited 19,302 times in 13,549 Documents Cited by ▼ Year ▼ Matrix computations. 3rd ed. Zbl 0865.65009 Golub, Gene; Van Loan, Charles F. 3,467 1996 Matrix computations. 2nd ed. Zbl 0733.65016 Golub, Gene H.; Van Loan, Charles F. 1,495 1989 Matrix computations. 4th ed. Zbl 1268.65037 Golub, Gene H.; Van Loan, Charles F. 1,265 2013 Numerical solution of saddle point problems. Zbl 1115.65034 Benzi, Michele; Golub, Gene H.; Liesen, Jörg 998 2005 Matrix computations. Zbl 0559.65011 Golub, Gene H.; Van Loan, Charles F. 938 1983 Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1036.65032 Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 688 2003 Generalized cross-validation as a method for choosing a good ridge parameter. Zbl 0461.62059 Golub, Gene H.; Heath, Michael; Wahba, Grace 489 1979 Calculation of Gauss quadrature rules. Zbl 0179.21901 Golub, Gene H.; Welsch, John H. 377 1969 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025 Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 369 2004 Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022 Bai, Zhongzhi; Golub, Gene H. 293 2007 Calculating the singular values and pseudo-inverse of a matrix. Zbl 0194.18201 Golub, G.; Kahan, W. 276 1965 A preconditioner for generalized saddle point problems. Zbl 1082.65034 Benzi, Michele; Golub, Gene H. 268 2004 A Hessenberg-Schur method for the problem AX+XB=C. Zbl 0421.65022 Golub, Gene H.; Nash, S.; Van Loan, Charles F. 268 1979 Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041 Elman, Howard C.; Golub, Gene H. 251 1994 A note on preconditioning for indefinite linear systems. Zbl 0959.65063 Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 243 2000 Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. Zbl 1079.65028 Bai, Zhong-Zhi; Golub, Gene H.; Lu, Lin-Zhang; Yin, Jun-Feng 229 2005 On direct methods for solving Poisson’s equations. Zbl 0217.52902 Buzbee, B. L.; Golub, G. H.; Nielson, C. W. 218 1970 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118 Chan, Tony F.; Golub, Gene H.; Mulet, Pep 207 1999 The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045 Golub, G. H.; Pereyra, V. 196 1973 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014 Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 193 2008 An analysis of the total least squares problem. Zbl 0468.65011 Golub, Gene H.; Van Loan, Charles F. 192 1980 Some modified matrix eigenvalue problems. Zbl 0254.65027 Golub, Gene H. 183 1973 SOR-like methods for augmented systems. Zbl 0991.65036 Golub, Gene H.; Wu, X.; Yuan, Jin-Yun 172 2001 Singular value decomposition and least squares solutions. Zbl 0181.17602 Golub, G. H.; Reinsch, C. 170 1970 Rank-one approximation to high order tensors. Zbl 1001.65036 Zhang, Tong; Golub, Gene H. 155 2001 Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034 Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 149 2007 Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II. Zbl 0099.10903 Golub, Gene H.; Varga, Richard S. 148 1961 Numerical methods for solving linear least squares problems. Zbl 0142.11502 Golub, G. 138 1965 On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1135.65016 Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 137 2008 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097 Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 136 2007 Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039 Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 131 2006 Methods for modifying matrix factorizations. Zbl 0289.65021 Gill, P. E.; Golub, G. H.; Murray, W.; Saunders, M. A. 126 1974 Numerical methods for computing angles between linear subspaces. Zbl 0282.65031 Björck, Åke; Golub, Gene H. 125 1973 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058 Chu, Moody T.; Golub, Gene H. 121 2005 Matrices, moments and quadrature with applications. Zbl 1217.65056 Golub, Gene H.; Meurant, Gérard 117 2010 Handbook series linear algebra. Linear least squares solutions by Householder transformations. Zbl 0142.11503 Businger, P.; Golub, G. H. 108 1965 A survey of matrix inverse eigenvalue problems. Zbl 0633.65036 Boley, Daniel; Golub, Gene H. 104 1987 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014 Golub, Gene; Pereyra, Victor 101 2003 Tikhonov regularization and total least squares. Zbl 0945.65042 Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 100 1999 Block preconditioning for the conjugate gradient method. Zbl 0556.65022 Concus, P.; Golub, G. H.; Meurant, G. 98 1985 Structured inverse eigenvalue problems. Zbl 1105.65326 Chu, Moody T.; Golub, Gene H. 90 2002 The direct solution of the discrete Poisson equation on irregular regions. Zbl 0231.65083 Buzbee, B. L.; Dorr, F. W.; George, J. A.; Golub, G. H. 85 1971 Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method. Zbl 0385.65048 Concus, P.; Golub, G. H.; O’Leary, D. P. 82 1978 On solving block-structured indefinite linear systems. Zbl 1036.65033 Golub, Gene H.; Greif, Chen 80 2003 Matrices, moments and quadrature. Zbl 0795.65019 Golub, G. H.; Meurant, Gerard 79 1994 Adaptive methods for the computation of PageRank. Zbl 1091.68044 Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 75 2004 The numerically stable reconstruction of a Jacobi matrix from spectral data. Zbl 0388.15010 de Boor, C.; Golub, G. H. 73 1978 Ill-conditioned eigensystems and the computation of the Jordan canonical form. Zbl 0341.65027 Golub, G. H.; Wilkinson, J. H. 70 1976 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015 Benzi, Michele; Gander, Martin J.; Golub, Gene H. 68 2003 Least-squares fitting of circles and ellipses. Zbl 0817.65008 Gander, Walter; Golub, Gene H.; Strebel, Rolf 64 1994 The Block Lanczos method for computing eigenvalues. Zbl 0407.68040 Golub, G. H.; Underwood, R. 63 1977 Iterative solution of linear systems. Zbl 0762.65019 Freund, Roland W.; Golub, Gene H.; Nachtigal, Noël M. 61 1992 Matrix computations. 3rd ed. Zbl 1118.65316 Golub, Gene; Van Loan, Charles F. 58 2007 An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053 Golub, Gene H.; Wathen, Andrew J. 55 1998 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017 Golub, Gene H.; Ye, Qiang 51 2002 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044 Calvetti, D.; Golub, G. H.; Reichel, L. 50 1999 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034 Golub, G. H.; Greif, C. 50 2006 Quadratically constrained least squares and quadratic problems. Zbl 0745.65029 Golub, Gene H.; von Matt, Urs 50 1991 Some large-scale matrix computation problems. Zbl 0870.65035 Bai, Zhaojun; Fahey, Mark; Golub, Gene 50 1996 Scientific computing. An introduction with parallel computing. Zbl 0790.65001 Golub, Gene; Ortega, James M. 50 1993 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022 Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 49 2000 The simplex method of linear programming using LU decomposition. Zbl 0181.19104 Bartels, R. H.; Golub, G. H. 49 1969 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054 Benzi, Michele; Golub, Gene H. 48 1999 Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Zbl 1068.65041 Bertaccini, Daniele; Golub, Gene H.; Serra Capizzano, Stefano; Tablino Possio, Cristina 48 2005 A stable numerical method for inverting shape from moments. Zbl 0956.65030 Golub, Gene H.; Milanfar, Peyman; Varah, James 47 2000 A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Zbl 0623.15020 Golub, G. H.; Hoffman, Alan; Stewart, G. W. 46 1987 Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050 Golub, G. H.; Meurant, G. 46 1997 Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. Zbl 0673.65017 Golub, Gene H.; O’Leary, Dianne P. 45 1989 A constrained eigenvalue problem. Zbl 0666.15006 Gander, Walter; Golub, Gene H.; von Matt, Urs 44 1989 Scientific computing and differential equations: an introduction to numerical methods. Rev. ed. Zbl 0749.65041 Golub, Gene H.; Ortega, James M. 43 1992 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022 Golub, Gene H.; Ye, Qiang 42 2000 Calculation of Gauss quadratures with multiple free and fixed knots. Zbl 0525.65010 Golub, G. H.; Kautsky, J. 41 1983 Eigenvalue computation in the 20th century. Zbl 0965.65057 Golub, Gene H.; van der Vorst, Henk A. 41 2000 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026 Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 40 1999 A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix. Zbl 0466.65022 Golub, Gene H.; Luk, Franklin T.; Overton, Michael L. 39 1981 On the solution of large, structured linear complementarity problems: the block partitioned case. Zbl 0391.90087 Cottle, Richard W.; Golub, Gene H.; Sacher, Richard S. 38 1978 On the calculation of Jacobi matrices. Zbl 0512.65030 Kautsky, J.; Golub, G. H. 36 1983 Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. Zbl 0245.65043 Concus, Paul; Golub, Gene H. 36 1973 Imposing curvature restrictions on flexible functional forms. Zbl 0573.62098 Gallant, A. Ronald; Golub, Gene H. 36 1984 Iterative methods for cyclically reduced non-self-adjoint linear systems. Zbl 0699.65021 Elman, Howard C.; Golub, Gene H. 34 1990 The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems. Zbl 0661.65033 Golub, Gene H.; Overton, Michael L. 32 1988 Note on the iterative refinement of least squares solution. Zbl 0156.16106 Golub, G. H.; Wilkinson, J. H. 32 1966 Estimates in quadratic formulas. Zbl 0822.65022 Golub, Gene H.; Strakoš, Zdeněk 32 1994 A generalized conjugate gradient method for nonsymmetric systems of linear equations. Zbl 0344.65020 Concus, Paul; Golub, Gene H. 31 1976 On Fourier-Toeplitz methods for separable elliptic problems. Zbl 0277.65065 Fischer, D.; Golub, G.; Hald, O.; Leiva, C.; Widlund, O. 31 1974 Using the QR factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for Markov chains. Zbl 0594.60072 Golub, Gene H.; Meyer, Carl D. jun. 31 1986 First international symposium on domain decomposition methods for partial differential equations (Proceedings, Paris, France, January 7-9, 1987). Zbl 0649.00019 30 1988 Regularization by truncated total least squares. Zbl 0891.65040 Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 30 1997 A rank-one reduction formula and its applications to matrix factorizations. Zbl 0844.65033 Chu, Moody T.; Funderlic, Robert E.; Golub, Gene H. 29 1995 Perturbation analysis of the canonical correlations of matrix pairs. Zbl 0811.15011 Golub, Gene H.; Zha, Hongyuan 28 1994 Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems. Zbl 1151.65027 Wu, Xiaonan; Golub, Gene H.; Cuminato, José A.; Yuan, Jin Yun 27 2008 A bibliography on semiseparable matrices. Zbl 1168.15312 Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. 27 2005 A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038 Botchev, Mike A.; Golub, Gene H. 27 2006 The restricted singular value decomposition: Properties and applications. Zbl 0738.15006 De Moor, Bart L. R.; Golub, Gene H. 27 1991 Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048 Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H. 26 2004 Matrix computations. Paperback ed., 4th printing. Zbl 0592.65011 Golub, Gene H.; Van Loan, Charles F. 26 1985 On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications. Zbl 0646.65033 Arbenz, Peter; Golub, Gene H. 25 1988 On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041 Golub, Gene H.; Vanderstraeten, Denis 25 2000 Tikhonov regularization for large scale problems. Zbl 0927.65058 Golub, Gene H.; von Matt, Urs 25 1998 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032 Golub, Gene H.; Ye, Qiang 24 2000 Matrix computations. 4th ed. Zbl 1268.65037 Golub, Gene H.; Van Loan, Charles F. 1,265 2013 Matrices, moments and quadrature with applications. Zbl 1217.65056 Golub, Gene H.; Meurant, Gérard 117 2010 Solving ellipsoid-constrained integer least squares problems. Zbl 1195.65049 Chang, Xiao-Wen; Golub, Gene H. 3 2010 The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments. Zbl 1169.65032 Golub, Gene; Uhlig, Frank 7 2009 A quasi-separable approach to solve the symmetric definite tridiagonal generalized eigenvalue problem. Zbl 1186.65046 Vandebril, Raf; Golub, Gene; van Barel, Marc 2 2009 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014 Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 193 2008 On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1135.65016 Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 137 2008 Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems. Zbl 1151.65027 Wu, Xiaonan; Golub, Gene H.; Cuminato, José A.; Yuan, Jin Yun 27 2008 Continuous methods for symmetric generalized eigenvalue problems. Zbl 1140.65029 Gao, Xing-Bao; Golub, Gene H.; Liao, Li-Zhi 9 2008 Approximation of the scattering amplitude and linear systems. Zbl 1188.65032 Golub, Gene H.; Stoll, Martin; Wathen, Andy 8 2008 Towards a backward perturbation analysis for data least squares problems. Zbl 1176.65047 Chang, X.-W.; Golub, G. H.; Paige, C. C. 2 2008 Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022 Bai, Zhongzhi; Golub, Gene H. 293 2007 Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034 Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 149 2007 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097 Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 136 2007 Matrix computations. 3rd ed. Zbl 1118.65316 Golub, Gene; Van Loan, Charles F. 58 2007 On the numerical condition of a generalized Hankel eigenvalue problem. Zbl 1121.65036 Beckermann, B.; Golub, G. H.; Labahn, G. 12 2007 Spectral analysis of a preconditioned iterative method for the convection-diffusion equation. Zbl 1140.65024 Bertaccini, Daniele; Golub, Gene H.; Serra-Capizzano, Stefano 12 2007 A hybrid approach combining Chebyshev filter and conjugate gradient for solving linear systems with multiple right-hand sides. Zbl 1151.65319 Golub, Gene H.; Ruiz, Daniel; Touhami, Ahmed 9 2007 A two-stage algorithm for computing PageRank and multistage generalizations. Zbl 1221.68041 Lee, Chris P.; Golub, Gene H.; Zenios, Stefanos A. 3 2007 A two-stage algorithm for computing pagerank and multistage generalizations. Zbl 1206.68050 Lee, Chris P.; Golub, Gene H.; Zenios, Stefanos A. 2 2007 Milestones in matrix computation. The selected works of Gene H. Golub. With commentaries by Anne Greenbaum, Åke Björk, Nicholas Higham, Walter Gautschi and G. W. Stewart. Edited by Raymond H. Chan, Chen Greif, and Dianne P. O’Leary. Zbl 1121.65031 Golub, Gene H. 1 2007 Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039 Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 131 2006 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034 Golub, G. H.; Greif, C. 50 2006 A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038 Botchev, Mike A.; Golub, Gene H. 27 2006 An algebraic analysis of a block diagonal preconditioner for saddle point systems. Zbl 1105.65048 Golub, Gene H.; Greif, Chen; Varah, James M. 17 2006 Continuous methods for extreme and interior eigenvalue problems. Zbl 1092.65029 Golub, Gene H.; Liao, Li-Zhi 13 2006 On a generalized eigenvalue problem for nonsquare pencils. Zbl 1128.15004 Chu, Delin; Golub, Gene H. 11 2006 Some observations on local least squares. Zbl 1103.65041 Bartels, R. H.; Golub, G. H.; Samavati, F. F. 1 2006 Numerical solution of saddle point problems. Zbl 1115.65034 Benzi, Michele; Golub, Gene H.; Liesen, Jörg 998 2005 Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. Zbl 1079.65028 Bai, Zhong-Zhi; Golub, Gene H.; Lu, Lin-Zhang; Yin, Jun-Feng 229 2005 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058 Chu, Moody T.; Golub, Gene H. 121 2005 Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Zbl 1068.65041 Bertaccini, Daniele; Golub, Gene H.; Serra Capizzano, Stefano; Tablino Possio, Cristina 48 2005 A bibliography on semiseparable matrices. Zbl 1168.15312 Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. 27 2005 The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach. Zbl 1100.65035 Boutry, Gregory; Elad, Michael; Golub, Gene H.; Milanfar, Peyman 19 2005 Multidimensional integral inversion, with applications in shape reconstruction. Zbl 1099.65128 Cuyt, Annie; Golub, Gene; Milanfar, Peyman; Verdonk, Brigitte 14 2005 How to deduce a proper eigenvalue cluster from a proper singular value cluster in the nonnormal case. Zbl 1088.65031 Serra-Capizzano, Stefano; Bertaccini, Daniele; Golub, Gene H. 12 2005 A bibliography on semiseparable matrices. Zbl 1168.15306 Van Barel, Marc; Vandebril, Raf; Golub, G.; Mastronardi, Nicola 8 2005 A subspace approximation method for the quadratic eigenvalue problem. Zbl 1079.65039 Holz, U. B.; Golub, G. H.; Law, K. H. 5 2005 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025 Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 369 2004 A preconditioner for generalized saddle point problems. Zbl 1082.65034 Benzi, Michele; Golub, Gene H. 268 2004 Adaptive methods for the computation of PageRank. Zbl 1091.68044 Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 75 2004 Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048 Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H. 26 2004 Shape from moments – an estimation theory perspective. Zbl 1369.62145 Elad, Michael; Milanfar, Peyman; Golub, Gene H. 16 2004 Semi-conjugate direction methods for real positive definite systems. Zbl 1052.65026 Yuan, J. Y.; Golub, G. H.; Plemmons, R. J.; Cecilio, W. A. G. 10 2004 Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription. Zbl 1491.92048 Alter, Orly; Golub, Gene H. 1 2004 Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1036.65032 Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 688 2003 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014 Golub, Gene; Pereyra, Victor 101 2003 On solving block-structured indefinite linear systems. Zbl 1036.65033 Golub, Gene H.; Greif, Chen 80 2003 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015 Benzi, Michele; Gander, Martin J.; Golub, Gene H. 68 2003 Scaling by binormalization. Zbl 1050.65049 Livne, Oren E.; Golub, Gene H. 8 2003 The spectrum of a modified linear pencil. Zbl 1054.65033 Elhay, S.; Golub, G. H.; Ram, Y. M. 2 2003 Structured inverse eigenvalue problems. Zbl 1105.65326 Chu, Moody T.; Golub, Gene H. 90 2002 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017 Golub, Gene H.; Ye, Qiang 51 2002 Symmetric-triangular decomposition and its applications. I: Theorems and algorithms. Zbl 1017.65020 Golub, Gene H.; Yuan, Jin-Yun 14 2002 Block orderings for tensor-product grids in two and three dimensions. Zbl 1002.65041 Golub, Gene H.; Greif, Chen; Varah, James M. 4 2002 Object-oriented parallel algorithms for computing three-dimensional isopycnal flow. Zbl 1014.76056 Concus, Paul; Golub, Gene H.; Sun, Yong 1 2002 SOR-like methods for augmented systems. Zbl 0991.65036 Golub, Gene H.; Wu, X.; Yuan, Jin-Yun 172 2001 Rank-one approximation to high order tensors. Zbl 1001.65036 Zhang, Tong; Golub, Gene H. 155 2001 From numerical analysis to computational science. Zbl 1047.65504 Engquist, Björn; Golub, Gene 16 2001 Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement. Zbl 1037.68784 Nguyen, Nhat; Milanfar, Peyman; Golub, Gene 15 2001 A computationally efficient superresolution image reconstruction algorithm. Zbl 1040.68567 Nguyen, Nhat; Milanfar, Peyman; Golub, Gene 11 2001 A parallel balance scheme for banded linear systems. Zbl 1055.65044 Golub, Gene H.; Sameh, Ahmed H.; Sarin, Vivek 6 2001 A note on preconditioning for indefinite linear systems. Zbl 0959.65063 Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 243 2000 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022 Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 49 2000 A stable numerical method for inverting shape from moments. Zbl 0956.65030 Golub, Gene H.; Milanfar, Peyman; Varah, James 47 2000 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022 Golub, Gene H.; Ye, Qiang 42 2000 Eigenvalue computation in the 20th century. Zbl 0965.65057 Golub, Gene H.; van der Vorst, Henk A. 41 2000 On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041 Golub, Gene H.; Vanderstraeten, Denis 25 2000 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032 Golub, Gene H.; Ye, Qiang 24 2000 Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations. Zbl 0948.65033 Golub, Gene H.; Zhang, Zhenyue; Zha, Hongyuan 16 2000 Computing the SVD of a general matrix product/quotient. Zbl 0969.65032 Golub, Gene; Sølna, Knut; Van Dooren, Paul 9 2000 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118 Chan, Tony F.; Golub, Gene H.; Mulet, Pep 207 1999 Tikhonov regularization and total least squares. Zbl 0945.65042 Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 100 1999 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044 Calvetti, D.; Golub, G. H.; Reichel, L. 50 1999 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054 Benzi, Michele; Golub, Gene H. 48 1999 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026 Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 40 1999 On some eigenvector-eigenvalue relations. Zbl 0929.15008 Elhay, S.; Gladwell, G. M. L.; Golub, G. H.; Ram, Y. M. 10 1999 An efficient algorithm for a bounded errors-in-variables model. Zbl 0957.65070 Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H. 8 1999 Subspace iterative methods for eigenvalue problems. Zbl 0932.65044 Zhang, T.; Golub, G. H.; Law, K. H. 2 1999 Applications and computation of orthogonal polynomials. Conference at the Mathematical Research Institute Oberwolfach, Germany, March 22–29, 1998. Dedicated to the memory of Günther Hämmerlin. Zbl 0919.00065 2 1999 A computable error bound for matrix functionals. Zbl 0937.65054 Calvetti, D.; Golub, G. H.; Reichel, L. 1 1999 An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053 Golub, Gene H.; Wathen, Andrew J. 55 1998 Tikhonov regularization for large scale problems. Zbl 0927.65058 Golub, Gene H.; von Matt, Urs 25 1998 Solution of biharmonic equations with application to radar imaging. Zbl 0933.65128 Andersson, Lars-Erik; Elfving, Tommy; Golub, Gene H. 24 1998 Parameter estimation in the presence of bounded data uncertainties. Zbl 0914.65147 Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H. 16 1998 A fast Poisson solver for the finite difference solution of the incompressible Navier-Stokes equations. Zbl 0957.76053 Golub, Gene H.; Huang, Lan Chieh; Simon, Horst; Tang, Wei-Pai 11 1998 Inner and outer iterations for the Chebyshev algorithm. Zbl 0911.65024 Giladi, Eldar; Golub, Gene H.; Keller, Joseph B. 8 1998 On the homotopy method for perturbed symmetric generalized eigenvalue problems. Zbl 0917.65035 Zhang, T.; Law, K. H.; Golub, G. H. 8 1998 Rank modifications of semidefinite matrices associated with a secant update formula. Zbl 0922.65031 Chu, Moody T.; Funderlic, R. E.; Golub, Gene H. 8 1998 Cyclic reduction – history and applications. Zbl 0921.65023 Gander, Walter; Golub, Gene H. 6 1998 Scientific computing, WSC ’97. Proceedings of the workshop held in Hong Kong, March 10–12, 1997. Zbl 0910.00057 2 1998 Efficient solution of the Jacobian system in Newton’s method close to a root. Zbl 0921.65039 Drexler, Michael; Golub, Gene H. 1 1998 Eigenvalue perturbation and generalized Krylov subspace method. Zbl 0931.65039 Zhang, T.; Golub, G. H.; Law, K. H. 1 1998 Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050 Golub, G. H.; Meurant, G. 46 1997 Regularization by truncated total least squares. Zbl 0891.65040 Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 30 1997 Generalized cross-validation for large scale problems. Zbl 0878.65032 Golub, Gene H.; von Matt, Urs 22 1997 Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Zbl 0883.15013 Bai, Zhaojun; Golub, Gene H. 18 1997 On a variational formulation of the generalized singular value decomposition. Zbl 0891.65038 Chu, Moody T.; Funderlic, Robert. E.; Golub, Gene H. 13 1997 150 years old and still alive: Eigenproblems. Zbl 0881.65026 van der Vorst, Henk A.; Golub, Gene H. 11 1997 Closer to the solution: Iterative linear solvers. Zbl 0881.65025 Golub, Gene H.; van der Vorst, Henk A. 10 1997 ...and 137 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 16,666 Authors 136 Reichel, Lothar 106 Wei, Yimin 69 Ma, Changfeng 68 Bai, Zhongzhi 68 Pan, Victor Yakovlevich 67 Huang, Ting-Zhu 64 Golub, Gene Howard 62 Zhang, Guofeng 57 Benner, Peter 57 Jódar Sanchez, Lucas Antonio 48 Khojasteh Salkuyeh, Davod 45 Ng, Michael Kwok-Po 45 Serra-Capizzano, Stefano 43 Van Barel, Marc 43 Van Dooren, Paul M. 42 Evans, David John 40 Jbilou, Khalide 40 Mehrmann, Volker 39 Simoncini, Valeria 38 Benzi, Michele 38 Dehghan Takht Fooladi, Mehdi 37 Axelsson, Axel Owe Holger 37 Liang, Zhaozheng 37 Wu, Shiliang 35 Jia, Zhongxiao 35 Li, Cuixia 34 Cao, Yang 34 Van Huffel, Sabine 33 Milovanović, Gradimir V. 33 Nakatsukasa, Yuji 32 Kressner, Daniel 32 Lin, Wen-Wei 32 Qi, Liqun 32 Wu, Yujiang 31 Chen, Guoliang 31 Li, Rencang 30 Huang, Zhengge 30 Yang, Aili 29 Jin, Xiaoqing 29 Wei, Musheng 28 Hajarian, Masoud 28 Sadkane, Miloud 28 Stoll, Martin 27 Cui, Jingjing 27 Mastronardi, Nicola 27 Saad, Yousef 26 Dai, Hua 26 Mitrouli, Marilena 26 Spalević, Miodrag M. 26 Vandebril, Raf 25 Chen, Fang 25 Martínez, José Mario 25 Wu, Gang 24 De Moor, Bart L. 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Mathematics 23 Mathematical Biosciences 23 Annals of Operations Research 23 Electronic Journal of Statistics ...and 697 more Serials all top 5 Cited in 61 Fields 8,584 Numerical analysis (65-XX) 2,832 Linear and multilinear algebra; matrix theory (15-XX) 1,355 Statistics (62-XX) 1,306 Operations research, mathematical programming (90-XX) 1,226 Partial differential equations (35-XX) 1,119 Computer science (68-XX) 966 Systems theory; control (93-XX) 831 Fluid mechanics (76-XX) 584 Information and communication theory, circuits (94-XX) 519 Mechanics of deformable solids (74-XX) 415 Calculus of variations and optimal control; optimization (49-XX) 414 Probability theory and stochastic processes (60-XX) 392 Approximations and expansions (41-XX) 364 Ordinary differential equations (34-XX) 332 Biology and other natural sciences (92-XX) 281 Operator theory (47-XX) 238 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 227 Combinatorics (05-XX) 207 Quantum theory (81-XX) 185 Dynamical systems and ergodic theory (37-XX) 179 Optics, electromagnetic theory (78-XX) 176 Harmonic analysis on Euclidean spaces (42-XX) 164 Special functions (33-XX) 159 Geophysics (86-XX) 148 Statistical mechanics, structure of matter (82-XX) 142 Mechanics of particles and systems (70-XX) 117 Integral equations (45-XX) 115 Algebraic geometry (14-XX) 98 Real functions (26-XX) 96 Functions of a complex variable (30-XX) 79 Number theory (11-XX) 76 Differential geometry (53-XX) 71 Functional analysis (46-XX) 67 Classical thermodynamics, heat transfer (80-XX) 60 Field theory and polynomials (12-XX) 57 Integral transforms, operational calculus (44-XX) 51 Commutative algebra (13-XX) 45 Difference and functional equations (39-XX) 42 Global analysis, analysis on manifolds (58-XX) 41 Potential theory (31-XX) 31 Convex and discrete geometry (52-XX) 30 Geometry (51-XX) 26 Astronomy and astrophysics (85-XX) 21 General and overarching topics; collections (00-XX) 21 Group theory and generalizations (20-XX) 20 History and biography (01-XX) 18 Measure and integration (28-XX) 18 Several complex variables and analytic spaces (32-XX) 18 Manifolds and cell complexes (57-XX) 17 General topology (54-XX) 14 Topological groups, Lie groups (22-XX) 13 Sequences, series, summability (40-XX) 10 Mathematical logic and foundations (03-XX) 10 Associative rings and algebras (16-XX) 9 Relativity and gravitational theory (83-XX) 7 Nonassociative rings and algebras (17-XX) 6 Algebraic topology (55-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Mathematics education (97-XX) 3 General algebraic systems (08-XX) 3 Abstract harmonic analysis (43-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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